What is the limit as h approaches 0 of ((1+h)^4-1)/h ?

The limit as h approaches 0 of ((1+h)^4-1)/h is 4

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limit as h approaches 0 of ((1+h)^4-1)/h

h \to 0 lim (\frac{( 1 + h ) ^{4} - 1}{h})

4

Solution steps

h \to 0 lim (\frac{( 1 + h ) ^{4} - 1}{h})

Simplify

\frac{( 1 + h ) ^{4} - 1}{h} : (h^{2} + 2 h + 2) (h + 2)

= h \to 0 lim ((h^{2} + 2 h + 2) (h + 2))

Plug in the value

h = 0

= (0^{2} + 2 \cdot 0 + 2) (0 + 2)

Simplify

(0^{2} + 2 \cdot 0 + 2) (0 + 2) : 4

= 4

\frac{d}{d x} (lo g_{e} (2 x))

\int - \frac{3}{x ^{2}} + 11 - 4^{x} d x

t^{2} \frac{d x}{d t} = \frac{1}{x ^{2}}, x (4) = 9

\frac{d}{d x} (3 x^{2} + 6 x + cos (x))

y^{^{'}} = tan (x) (sec (x))^{4}

What is the limit as h approaches 0 of ((1+h)^4-1)/h ?
The limit as h approaches 0 of ((1+h)^4-1)/h is 4